At the end of the previous chapter we drew attention to the work of T.C. Wallstrom [1]} who objected to the equivalence of Nelson's stochastic mechanics with standard quantum theory. Essentially, the issue there was that to recover the full complex Hilbert space of physical states from the real-valued \(\rho \)  and \(\Phi \) , one must simultaneous require the phase \(\Phi \)  to be multi-valued all while the complex \(\Psi \)  remain single valued. The argument, ultimately, was an empirical one: deny multi-valued \(\Phi \)  and you deny the experimentally verified, non-vanishing values of angular momentum.
